When the following equation is balanced with the smallest integral coefficients, the coefficient of the HNO3 is

Li2CO3(s) +HNO3(aq) -- LiNO3(aq)+H2O(l)+CO2

Li2CO3(s) + 2HNO3(aq) -- 2LiNO3(aq)+H2O(l)+CO2

To balance the equation, we need to ensure that the number of atoms of each element is the same on both sides of the equation.

Let's count the number of atoms for each element in the equation:

On the left side:
Li: 2
C: 1
O: 3
H: 1
N: 1

On the right side:
Li: 1
N: 1
O: 3
H: 2
C: 1

To balance the number of atoms, we can start with the elements that are not balanced and adjust their coefficients accordingly.

Let's start with nitrogen (N). There is only one nitrogen atom on both sides of the equation. Therefore, the coefficient of HNO3 remains 1.

Now, let's focus on hydrogen (H). On the left side, there is one hydrogen atom, and on the right side, there are two hydrogen atoms. To balance hydrogen, we need to put a coefficient of 2 in front of HNO3:

Li2CO3(s) + 2HNO3(aq) -- LiNO3(aq) + H2O(l) + CO2

Finally, let's check the other elements. Both Li (lithium), C (carbon), and O (oxygen) are already balanced, as there is only one atom of each on both sides of the equation.

Therefore, the coefficient of HNO3 is 2.